Finite Group Databasebeta

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C₂×#60806 #10575510

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• rational
• ambivalent

Aliases

Subgroups

8318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,9)(6,8)(7,10)(11,12)(13,16)(14,17)(15,18)(19,22)(20,24)(21,23)(25,26);(3,5,6,10)(4,7,8,9)(11,13)(12,16)(14,21)(15,20)(17,23)(18,24)(19,25)(22,26);(5,10)(7,9)(12,17)(14,22)(16,23)(18,19)(21,26)(24,25);(4,8)(7,9)(13,20)(16,24)(21,26)(23,25);(12,18)(16,24)(17,19)(23,25)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482706);